.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_reliability_sensitivity/reliability/plot_probability_simulation_results.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_reliability_sensitivity_reliability_plot_probability_simulation_results.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_reliability_sensitivity_reliability_plot_probability_simulation_results.py:


Exploitation of simulation algorithm results
============================================

.. GENERATED FROM PYTHON SOURCE LINES 7-15

In this example we are going to retrieve all the results proposed by probability simulation algorithms:

- the probability estimate
- the estimator variance
- the confidence interval
- the convergence graph of the estimator
- the stored input and output numerical samples
- importance factors

.. GENERATED FROM PYTHON SOURCE LINES 17-22

.. code-block:: Python

    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pyplot as plt









.. GENERATED FROM PYTHON SOURCE LINES 23-24

Create the joint distribution of the parameters.

.. GENERATED FROM PYTHON SOURCE LINES 26-31

.. code-block:: Python

    distribution_R = ot.LogNormalMuSigma(300.0, 30.0, 0.0).getDistribution()
    distribution_F = ot.Normal(75e3, 5e3)
    marginals = [distribution_R, distribution_F]
    distribution = ot.JointDistribution(marginals)








.. GENERATED FROM PYTHON SOURCE LINES 32-33

Create the model.

.. GENERATED FROM PYTHON SOURCE LINES 35-37

.. code-block:: Python

    model = ot.SymbolicFunction(["R", "F"], ["R-F/(pi_*100.0)"])








.. GENERATED FROM PYTHON SOURCE LINES 38-42

.. code-block:: Python

    modelCallNumberBefore = model.getEvaluationCallsNumber()
    modelGradientCallNumberBefore = model.getGradientCallsNumber()
    modelHessianCallNumberBefore = model.getHessianCallsNumber()








.. GENERATED FROM PYTHON SOURCE LINES 43-44

To have access to the input and output samples after the simulation, activate the History mechanism.

.. GENERATED FROM PYTHON SOURCE LINES 46-48

.. code-block:: Python

    model = ot.MemoizeFunction(model)








.. GENERATED FROM PYTHON SOURCE LINES 49-51

Remove all the values stored in the history mechanism.
Care : it is done regardless the status of the History mechanism.

.. GENERATED FROM PYTHON SOURCE LINES 53-55

.. code-block:: Python

    model.clearHistory()








.. GENERATED FROM PYTHON SOURCE LINES 56-57

Create the event whose probability we want to estimate.

.. GENERATED FROM PYTHON SOURCE LINES 59-63

.. code-block:: Python

    vect = ot.RandomVector(distribution)
    G = ot.CompositeRandomVector(model, vect)
    event = ot.ThresholdEvent(G, ot.Less(), 0.0)








.. GENERATED FROM PYTHON SOURCE LINES 64-65

Create a Monte Carlo algorithm.

.. GENERATED FROM PYTHON SOURCE LINES 67-73

.. code-block:: Python

    experiment = ot.MonteCarloExperiment()
    algo = ot.ProbabilitySimulationAlgorithm(event, experiment)
    algo.setMaximumCoefficientOfVariation(0.1)
    algo.setMaximumStandardDeviation(0.001)
    algo.setMaximumOuterSampling(int(1e4))








.. GENERATED FROM PYTHON SOURCE LINES 74-76

Define the HistoryStrategy to store the values of :math:`P_n` and :math:`\sigma_n` used ot draw the convergence graph.
Compact strategy : N points

.. GENERATED FROM PYTHON SOURCE LINES 78-82

.. code-block:: Python

    N = 1000
    algo.setConvergenceStrategy(ot.Compact(N))
    algo.run()








.. GENERATED FROM PYTHON SOURCE LINES 83-84

Retrieve result structure.

.. GENERATED FROM PYTHON SOURCE LINES 86-88

.. code-block:: Python

    result = algo.getResult()








.. GENERATED FROM PYTHON SOURCE LINES 89-90

Display the simulation event probability.

.. GENERATED FROM PYTHON SOURCE LINES 92-94

.. code-block:: Python

    result.getProbabilityEstimate()





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    0.030580075662042867



.. GENERATED FROM PYTHON SOURCE LINES 95-96

Criteria 3 : Display the Standard Deviation of the estimator

.. GENERATED FROM PYTHON SOURCE LINES 96-98

.. code-block:: Python

    result.getStandardDeviation()





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    0.003057093060511293



.. GENERATED FROM PYTHON SOURCE LINES 99-100

Display the variance of the simulation probability estimator.

.. GENERATED FROM PYTHON SOURCE LINES 102-104

.. code-block:: Python

    result.getVarianceEstimate()





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    9.345817980626304e-06



.. GENERATED FROM PYTHON SOURCE LINES 105-106

Criteria 2 : Display the number of iterations of the simulation

.. GENERATED FROM PYTHON SOURCE LINES 106-108

.. code-block:: Python

    result.getOuterSampling()





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    3172



.. GENERATED FROM PYTHON SOURCE LINES 109-110

Display the total number of evaluations of the model

.. GENERATED FROM PYTHON SOURCE LINES 110-112

.. code-block:: Python

    result.getOuterSampling() * result.getBlockSize()





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    3172



.. GENERATED FROM PYTHON SOURCE LINES 113-114

Save the number of calls to the model, its gradient and hessian done so far.

.. GENERATED FROM PYTHON SOURCE LINES 116-120

.. code-block:: Python

    modelCallNumberAfter = model.getEvaluationCallsNumber()
    modelGradientCallNumberAfter = model.getGradientCallsNumber()
    modelHessianCallNumberAfter = model.getHessianCallsNumber()








.. GENERATED FROM PYTHON SOURCE LINES 121-122

Display the number of iterations executed and the number of evaluations of the model.

.. GENERATED FROM PYTHON SOURCE LINES 124-126

.. code-block:: Python

    modelCallNumberAfter - modelCallNumberBefore





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    3172



.. GENERATED FROM PYTHON SOURCE LINES 127-128

Get the mean point in event  domain care : only for Monte Carlo and LHS sampling methods.

.. GENERATED FROM PYTHON SOURCE LINES 130-132

.. code-block:: Python

    result.getMeanPointInEventDomain()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=2 values=[245.843,80222]
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 133-134

Get the associated importance factors care : only for Monte Carlo and LHS sampling methods.

.. GENERATED FROM PYTHON SOURCE LINES 136-138

.. code-block:: Python

    result.getImportanceFactors()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=PointWithDescription name=Unnamed dimension=2 description=[X0,X1] values=[0.776373,0.223627]
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 139-142

.. code-block:: Python

    graph = result.drawImportanceFactors()
    view = viewer.View(graph)




.. image-sg:: /auto_reliability_sensitivity/reliability/images/sphx_glr_plot_probability_simulation_results_001.svg
   :alt: Importance Factors from Simulation - v0
   :srcset: /auto_reliability_sensitivity/reliability/images/sphx_glr_plot_probability_simulation_results_001.svg
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 143-150

Display the confidence interval length centered around the MonteCarlo probability. The confidence interval is

.. math::
   IC = [\tilde{p} - 0.5 \ell, \tilde{p} + 0.5 \ell]


with level 0.95, where :math:`\tilde{p}` is the estimated probability and :math:`\ell` is the confidence interval length.

.. GENERATED FROM PYTHON SOURCE LINES 152-163

.. code-block:: Python

    probability = result.getProbabilityEstimate()
    length95 = result.getConfidenceLength(0.95)
    print("0.95 Confidence Interval length = ", length95)
    print(
        "IC at 0.95 = [",
        probability - 0.5 * length95,
        "; ",
        probability + 0.5 * length95,
        "]",
    )





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    0.95 Confidence Interval length =  0.011983584591978923
    IC at 0.95 = [ 0.024588283366053405 ;  0.03657186795803233 ]




.. GENERATED FROM PYTHON SOURCE LINES 164-165

Draw the convergence graph and the confidence interval of level alpha. By default, alpha = 0.95.

.. GENERATED FROM PYTHON SOURCE LINES 167-171

.. code-block:: Python

    alpha = 0.90
    graph = algo.drawProbabilityConvergence(alpha)
    view = viewer.View(graph)




.. image-sg:: /auto_reliability_sensitivity/reliability/images/sphx_glr_plot_probability_simulation_results_002.svg
   :alt: ProbabilitySimulationAlgorithm convergence graph at level 0.9
   :srcset: /auto_reliability_sensitivity/reliability/images/sphx_glr_plot_probability_simulation_results_002.svg
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 172-173

Get the numerical samples of the input and output random vectors stored according to the History Strategy specified and used to evaluate the probability estimator and its variance.

.. GENERATED FROM PYTHON SOURCE LINES 175-179

.. code-block:: Python

    inputSampleStored = model.getInputHistory()
    outputSampleStored = model.getOutputHistory()
    inputSampleStored






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table>
      <tr><td></td><th>v0</th><th>v1</th></tr>
      <tr><th>0</th><td>317.1822</td><td>68669.13</td></tr>
      <tr><th>1</th><td>285.7421</td><td>81027.39</td></tr>
      <tr><th>2</th><td>240.1374</td><td>76750.21</td></tr>
    <tr><td colspan="3">...</td></tr>
      <tr><th>3169</th><td>266.9563</td><td>74830.12</td></tr>
      <tr><th>3170</th><td>282.285</td><td>78480.19</td></tr>
      <tr><th>3171</th><td>247.1724</td><td>81708.23</td></tr>
    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 180-181

Get the values of the estimator and its variance stored according to the History Strategy specified and used to draw the convergence graph.

.. GENERATED FROM PYTHON SOURCE LINES 183-187

.. code-block:: Python

    estimator_probability_sample = algo.getConvergenceStrategy().getSample()[0]
    estimator_variance_sample = algo.getConvergenceStrategy().getSample()[1]
    print(estimator_probability_sample, estimator_variance_sample)
    plt.show()




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    [0,-1] [0.25,0.046875]





.. _sphx_glr_download_auto_reliability_sensitivity_reliability_plot_probability_simulation_results.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_probability_simulation_results.ipynb <plot_probability_simulation_results.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_probability_simulation_results.py <plot_probability_simulation_results.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_probability_simulation_results.zip <plot_probability_simulation_results.zip>`